考虑材料性能不确定性的声振强耦合系统稳健拓扑优化  

Robust topology optimization of strongly coupled structural-acoustic systems considering material properties uncertainty

作　　者：郑文治 陈海波[1] 操小龙[2] ZHENG Wenzhi;CHEN Haibo;CAO Xiaolong(CAS Key Laboratory of Mechanical Behavior and Design of Materials,Department of Modern Mechanics,University of Science and Technology of China,Hefei 230027,China;Beijing Research Institute of Mechanical and Electrical Engineering,Beijing 100074,China)

机构地区：[1]中国科学技术大学近代力学系中国科学院材料力学行为与设计重点实验室,合肥230027 [2]北京机电工程研究所,北京100074

出　　处：《振动与冲击》2023年第22期93-102,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金(12172350);中国科学院战略性先导科技专项(B类)子课题(XDB22040502)。

摘　　要：针对外声场与结构强耦合问题,亟待开展不确定性优化的发展需求,提出了一种考虑材料性能不确定性的稳健拓扑优化设计方法。采用随机场模型描述材料弹性模量的不确定性,用级数最优线性估值方法将其离散成不相关的随机变量;进而用混沌多项式展开(polynomial chaos expansion,PCE)方法结合有限元-边界元耦合方法进行随机响应分析。通过材料属性的有理近似模型描述双材料的分布,以辐射声功率级的均值和标准差的加权和作为稳健拓扑优化的目标函数,随机响应的灵敏度同样通过PCE方法获得,最后通过移动渐近线优化算法对优化问题进行求解。数值算例表明,该方法相较于确定性拓扑优化可以获得对材料弹性模量不确定性更加不敏感的设计,这是不确定性优化方法在含外声场的声振强耦合问题上的一个新的拓展研究。For dealing with the strongly coupling problem between an external acoustic field and a structure,there is an urgent need for the development of uncertainty optimization technology.A robust topology optimization method considering the uncertainty of material performance was presented.A random field model was used to describe the uncertainty of the elastic modulus of the material,and the expansion optimal linear estimation method was used to discretize it into uncorrelated random variables.The polynomial chaos expansion(PCE) method was combined with the finite element-boundary element coupling method for the random response analysis.The rational approximation of material properties model was used to describe the distribution of bi-material.A weighted sum of the mean and standard deviation of the radiation sound power level was set as the objective function for robust topology optimization.The sensitivity of the random response was also obtained by the PCE method,and then the optimization problem was solved by the method of moving asymptotes.The numerical examples show that the proposed method can give a design scheme that is less sensitive to the uncertainty of elastic modulus than the deterministic topology optimization.It is a new extension of uncertain optimization methods to strongly coupling problems between the external acoustic field and structure.

关 键 词：声振耦合系统 拓扑优化 稳健设计 混沌多项式展开(PCE) 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3